Averages, Creativity and AI

Average and novel?

The average height of all passengers on a train was calculated to be 165 cm. Yet, not a single person on that train was 165 cm tall. In fact, most people were actually far from that height. There was no average height passenger. And consider the average passenger more globally, factoring in multiple characteristics such as height, weight, eye color, etc. Such a person likely does not exist anywhere—not in the train nor elsewhere.

The point is: "average" does not mean "has been seen". Synthesizing or averaging old facts, something new and previously unseen is (likely to be) created. To practice this intuition, consider the following visual scenarios. The first is very close to the train example. The second one is more extreme, and we see that all passengers may actually be far from the average. And this second scenario is not at all impossible. Suppose that there are lots of families in this train, with parents and young children. There may be people far below the average and people far above the average, without anyone necessarily being in the middle.

Average and extreme?

Is this novelty merely unspectacular, doom to fall in the middle of a large group and not yielding new or personalized territories? Not necessarily. In a primary school, the average height is low, compared to the general population. In a basketball academy, the average height might be extraordinarily tall. If we can gear the system to compute one or the other average, we can adjust the output to our target of interest. The average of a subgroup, may be extreme with respect to the whole group.

Consider the second example from above again. If we can select the group on the left, we will obtain a low average (left image below). If we can select the group on the right, we will obtain a high average (right image below). That is, focussing on specific domains, we can obtain averages that are biased in the direction we may like. This is in essence what prompt engineering allows.

Average and AI

These two forces can explain why a simple averaging system can produce novelty and can produce extreme results. If AI systems may simply synthetize past data in this way, it may nonetheless create new results, and we can manipulate them to create extreme results. By carefully engineering prompts, one can influence AI outputs to lean toward certain desired characteristics, even if extreme.

Modern AI systems may be more complicated than averaging machines. They may do weighted averages, or non-linear aggregations of other sorts. This is part of what makes them unpredicatble, and in fact ill-understood, but their creativity and ability to obtain extreme values may not be driven by complex mechanisms, and may be present in much more primitive systems.